Eigensets of switching dynamical systems
Dynamical Systems
2026-01-21 v1 Metric Geometry
Optimization and Control
Abstract
Reachability sets of linear switching dynamical systems (systems of ODE with time-dependent matrices that take values from a given compact set) are analysed. An eigenset is a non-trivial compact set M that possesses the following property: the closure of the set of points reachable by trajectories starting in M in time t is equal to exp(at)M. This concept introduced in a recent paper of E.Viscovini is an analogue of an eigenvector for compact sets of matrices. We prove the existence of eigensets, analyse their structure and properties, and find ``eigenvalues'' a for an arbitrary system. The question which compact sets, in particular, which convex sets and polyhedra, can be presented as eigensets of suitable systems, is studied.
Cite
@article{arxiv.2601.13990,
title = {Eigensets of switching dynamical systems},
author = {Vladimir Protasov},
journal= {arXiv preprint arXiv:2601.13990},
year = {2026}
}